Question

A line segment has endpoints at `(9 ,2 )` and `(7 , 4)`. The line segment is dilated by a factor of `4` around `(1 , 5)`. What are the new endpoints and length of the line segment?

Answer 1

`color(orange)("New coordinates are " (33,-7), (-25, 1)`

`color(orange)("Length of the line segment '" = sqrt((33-25)^2 + (-7-1)^2) ~~ 11.3137`

Explanation:

`A(8,4), B(9,2), " about point " D (1,5), " dilation factor "4`

`A'((x),(y)) =(4)a - (3)d =(4)*((9),(2)) - (3)*((1),(5)) = ((33),(-7))`

`B'((x),(y)) = (4)b - (3)d = (4)*((7),(4)) - (3)*((1),(5)) = ((25),(1))`

`color(orange)("New coordinates are " (33,-7), (-25, 1)`

`color(orange)("Length of the line segment '" = sqrt((33-25)^2 + (-7-1)^2) ~~ 11.3137`